Ozan Öktem

Ozan Öktem researches methods for solving inverse problems, where the goal is to recreate the input to a simulator so that it generates output matching observations. Solving an inverse problem is akin to running a simulator "in reverse."

Inverse problems arise in numerous applications such as tomography, microscopy, remote sensing, and radar/sonar. A challenge in solving inverse problems is that they are ill-posed, meaning the solution can drastically change due to a very small measurement error in the observations. Since measurement errors are practically unavoidable, the solution method must be designed in such a way that one can be confident the computed solution is sensible. This is achieved through regularization, a mathematical framework for incorporating prior known information about the solution.

Ozan and his research group have developed methods for solving inverse problems that combine deep learning with classical applied mathematics. These methods have been successfully applied to low-dose tomography. Another development pertains to regularization methods that use shape information, which has proven to be powerful for 3D electron microscopy of proteins. These methods are also applied to tomographic imaging of moving organs.